construct a truth table for each of the following arguments and indicate whether

Question

construct a truth table for each of the following arguments and indicate whether the argument is valid or invalid.

1.  a v (b & c)

~ (b & c)

a

Traslate into symbols, construct a truth table and determine its validity

1. UN peacekeepers will not attack the local militants, provided that the militants behave themselves. The militants will not make trouble if the UN peacekeepers don't attack. Therefore, UN peacekeepers will not attack the local militants and the militants will not make trouble.

2. "If then, it is agreed that things are either the result of coincidence or for an end, and these cannot be the result of coincidence or spontaneity, it follows that they must be for an end,"

Explanation / Answer

We see that in rows 2,3 and 4, both ~(b&c) and av(b&c) are true and a is also true.

Thus the conclusion is valid.

1. p:UN peacekeepers will not attack the local militants.

q: The militants will not make trouble / The militants behave themselves.

Given statements are

q -> p

p -> q

Therefore p ^ q

In the last row, both p->q and q->p are true but p^q is false.

So the statement is invalid.

2. p: Things are the result of coincidence

q: Things are for an end

r: Things are result of spontaneity

The given statements are

p v q

~(pvr)

Therefore q

From the table, (pvq) and ~(pvr) are both true in only row 6 when q is also true.

So the conclusion is valid.

a b c b&c ~(b&c) av(b&c) T T T T F T T T F F T T T F T F T T T F F F T T F T T T F T F T F F T F F F T F T F F F F F T F

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